While still in the university I remember some people mentioning how chaos theory and fractals could be applied in a finance context.

The topic has kind of escaped my radar until now. Usually I am quite skeptical when it comes to the application of new research to quant finance. Often the added value isn’t significant but the increase in complexity is. It starts with some famous researching mentioning how some purely theoretical concept might be applied e.g. in pricing derivatives. This precipitates a small landslide of academic research (mostly done by PhD students).
After a while people in finance notice those ideas and try first implementations which then show the added benefit to be only marginal.

As I seet it generally two aspects of chaos theory could be suited for
a financial application:

spontaneous order (might be used to model how market prices come to pass)

distinguishing between random and chaotic data (might be usefuly when dealing with financial time series)